4 - Vector Preliminaries and Constructing a Basis

Summary

I start by invoking the ‘fundamental rule of calculus notation’ to ensure the correct translation of an English sentence into the language of calculus. As examples, I derive the ‘rocket equation’ and the standard expression for the gravitational potential of a sphere. I discuss the importance of treating units properly. I make the important point that a frame is not the same as a system of coordinates. I distinguish between ‘proper vectors’ and ‘coordinates vectors’, which is needed for a proper understanding of transforming coordinates. Because the study of vehicle attitude is built on basis vectors, I show how to construct these from both an intuitive viewpoint and a purely mathematical viewpoint.